“Do we then overthrow the law by this faith? By no means! On the contrary, we uphold the law.”
-Romans 3:31, ESV
Romans 3:31 is a proof text and pillar for Covenant Theology’s (CT) insistence for the ‘third use’ of the Law. On the face of it, and within the framework of CT, it is not difficult to see how this verse lends itself to such an understanding. Confessedly, I once saw this verse as a reason to refute the claims of NCT’s view of Mosaic Law. However, three considerations make clear that CT’s view of this verse erroneous.
1. Romans 3:31 cannot oppose what Paul writes elsewhere concerning Mosaic Law & the Christian (e.g. Romans 6-8; 10:4; 2 Cor. 3; Galatians 3-5, Ephesians 2:14-15; Col. 2:14). This is to say nothing of the clear testimony of Hebrews 8-10. To pit Romans 3:31 against the weight and clear teaching of the rest of Scripture is unsound theological method. Paul would not assert one thing in Galatians (namely, freedom from the entire Mosaic legislation) only to contradict himself later in Romans. A high view of Scripture guards against such absurdity since God, the Author of Scripture, is a God of truth. Therefore, since truth by definition is non-contradictory, Paul is not at odds with himself. Romans 3:31 cannot undermine, or fly in the face of, what the apostle writes elsewhere. The veracity of Scripture as a whole is at stake here.
2. The immediate context does not support CT’s confidence. A few verses earlier, in Romans 3:21, Paul states that although justifying righteousness has been manifested apart from the law, the “Law and the Prophets bear witness to it.” The next phrase makes it clear; faith in Christ for righteousness is that to which “the Law and Prophets” bear witness. Therefore, in 3:31, the apostle may simply be saying that faith in Christ for righteousness upholds that OT law which calls for faith (cf. John 5:46; Romans 10:6ff; Deut. 30:11ff.). Of course, called into question here is the precise referent of ‘law.’ Does ‘law,’ a word with a wide semantic range, mean the Mosaic Covenant? The Ten Commandments? The Pentateuch? The entire Old Testament? Exegesis, not eisogesis, must rule. To simply read a theological category into this is bad hermeneutical method. Care must be taken to not define the occurrence of a word too narrowly or broadly.
3. But assuming, for argument’s sake, ‘law’ in Romans 3:31 refers to the Mosaic Covenant only, we need not conclude Paul teaches that law remains in force for the one who has faith in Christ. A simple reading of the verse, allowing it to speak in context (3:21-31) makes it clear Paul teaches no such thing. “Do we then overthrow the law by this faith?” is a question posed in a specific context, one in which the Law, in full force, is brought to bear on Christ. Christ is its satisfaction (3:25). Christ, by His redemption-accomplishing, wrath-appeasing, justice-satisfying death, fulfilled the law with its precepts and punishments. And He did so for us, for everyone who would ever believe in Him for justification. As Douglas Moo once wrote: “Justification takes full account of the law, providing for its complete satisfaction in believers through their incorporation into Christ.” The irony of ironies is this: we uphold the law by looking away from it and to Christ, the One who kept it. The work of Christ, and faith in Him, takes seriously, and into full consideration, the Law. This satisfies the grammar. This satisfies the contexts, both near and far. And that, dear reader, satisfies and cheers my soul!
Romans 3:31 is no obstacle to the position that sees Christ as the fullfilment of all things Old Testament, freeing the New Covenant believer to be led by a new kind of “Law” (i.e. the Law of Christ).
 For an influential example, see John Murray’s “Law & Grace.” Available at http://www.the-highway.com/lawgrace.html